On the compound Poisson phase-type process and its application in shock models
In this paper, the compound Poisson phase-type process is defined and analyzed. This paper proves that for a non-negative compound Poisson phase-type process, the compound value for all the arrivals by a given time can be approximated by a phase-type distribution. As an application of this process,...
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| Published in | Journal of computational and applied mathematics Vol. 446; p. 115852 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier B.V
15.08.2024
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| Subjects | |
| Online Access | Get full text |
| ISSN | 0377-0427 1879-1778 |
| DOI | 10.1016/j.cam.2024.115852 |
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| Abstract | In this paper, the compound Poisson phase-type process is defined and analyzed. This paper proves that for a non-negative compound Poisson phase-type process, the compound value for all the arrivals by a given time can be approximated by a phase-type distribution. As an application of this process, three different shock models are studied: the cumulative shock model, a degradation-threshold-shock model, and a shock model for the multi-component system. A novel approach is proposed to compute the system’s reliability under the aforementioned shock models for a general counting process. Numerical illustrations are presented. |
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| AbstractList | In this paper, the compound Poisson phase-type process is defined and analyzed. This paper proves that for a non-negative compound Poisson phase-type process, the compound value for all the arrivals by a given time can be approximated by a phase-type distribution. As an application of this process, three different shock models are studied: the cumulative shock model, a degradation-threshold-shock model, and a shock model for the multi-component system. A novel approach is proposed to compute the system’s reliability under the aforementioned shock models for a general counting process. Numerical illustrations are presented. |
| ArticleNumber | 115852 |
| Author | Xie, Min Goyal, Dheeraj |
| Author_xml | – sequence: 1 givenname: Dheeraj orcidid: 0000-0002-5079-5185 surname: Goyal fullname: Goyal, Dheeraj email: dheerajgoyal6897@gmail.com organization: Centre for Intelligent Multidimensional Data Analysis Limited, Hong Kong Science Park, Hong Kong – sequence: 2 givenname: Min surname: Xie fullname: Xie, Min email: minxie@cityu.edu.hk organization: Centre for Intelligent Multidimensional Data Analysis Limited, Hong Kong Science Park, Hong Kong |
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| Cites_doi | 10.1017/jpr.2020.103 10.1017/S0269964822000195 10.1016/j.ejor.2017.05.049 10.1016/j.ress.2021.107937 10.1098/rspa.2010.0384 10.1016/j.ejor.2015.11.032 10.1109/ACCESS.2020.2976200 10.1016/j.ress.2019.03.045 10.1016/j.spl.2019.04.008 10.1016/j.ress.2022.108911 10.1007/s11749-023-00864-z 10.1016/j.ress.2022.108876 10.1007/s11009-022-09961-2 10.1080/24725854.2019.1567958 10.1016/j.ress.2018.01.006 10.1016/j.cam.2018.12.011 10.1016/j.ress.2018.07.032 10.1016/j.ress.2023.109420 10.2307/3213143 10.1080/17442508.2020.1868469 10.1016/j.cam.2023.115364 10.1007/s11749-023-00867-w 10.1007/s11009-021-09880-8 10.1080/0740817X.2010.491502 10.1016/j.ress.2023.109671 10.1239/aap/1418396247 |
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